probability Q..pls answer

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Inspired: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sun May 24, 2009 7:27 am; Location: Glasgow

by Inspired » Thu Jan 14, 2010 11:12 am

If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one odd number?

1/8
1/4
1/2
3/4
7/8

pls ans with explanation

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Source: Beat The GMAT — Problem Solving | Thu Jan 14, 2010 11:12 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 14, 2010 11:25 am

Inspired wrote:If a six sided die is rolled three times, what is the probability of getting at least one even number and at least one odd number?

1/8
1/4
1/2
3/4
7/8

pls ans with explanation

For questions involving "at least" it is often useful to use the complement.
That is: P(event A occurs) = 1 - P(event A does not occur)

In your question, what would it mean if your event (at least one even and one odd) does not occur?
It would mean we have either all odds or all evens.

So, we are looking for 1 - P(all odd or all even)

P(all odd OR all even) = P(all odd) + P(all even)

Begin with P(all odd)
What is the probability that all three numbers are odd?
Well, the probability that the first roll is odd = 3/6 = 1/2
The probability that the 2nd roll is odd = 1/2
The probability that the 3rd roll is odd = 1/2
So, P(1st is odd AND 2nd is odd AND 3rd is odd) = 1/2 x 1/2 x 1/2 = 1/8

We can perform similar calculations to see that P(all even) = 1/8

So, P(all odd OR all even) = P(all odd) + P(all even)
= 1/8 + 1/8
= 1/4

So, 1 - P(all odd or all even) = 1 -1/4 = 3/4 (D)

Brent Hanneson - Creator of GMATPrepNow.com

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Inspired: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Sun May 24, 2009 7:27 am; Location: Glasgow

by Inspired » Thu Jan 14, 2010 11:35 am

thank you very much for your detailed explanation. I am now clear about AND and OR operators too.

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